The empirical results indicate that the spot and future prices of used commodities are stationary after the first differencing but the spot and future price of natural gas had the stationarity even before doing the first differencing.
The major findings of the study are as follows:
The Johansen cointegration test exhibits that that there exist the long run relationship between the spot and future prices of the agricultural, energy and precious metals (commodities) except the crude oil spot and future prices.
Thus, the first hypothesis is fulfilled.
The granger causality test exhibits the bi-directional, uni-directional and no causality relationship between the selected spot-future, future-spot, spot-spot and future-future prices of the commodities. In the case of agricultural commodities (cocoa and coffee), energy (crude oil) and precious metal (gold) bi-directional relationship was found whereas at the same time natural gas spot and silver future have the uni-directional relationship with the natural gas future price and silver spot price respectively. Thus, it is safely concluded that although in the theories future prices play a crucial role in the price discovery process, the spot price too play an equal role in this respect. In this way, the second hypothesis is also explained and fulfilled with the notion that prices of one variable granger causes the price of another variable.
Finally, the VAR model explained the interrelationship among the prices of the variables in the system when the shocks are given. It highlights the fact that the movement in the dependent variable occurs which is caused due to its own shock. Moreover, the VAR model results the proportion of effect is high in the case of the respective spot and future of the commodities rather than among the prices of the commodities meaning the changes of movement is seen between the spot vs. spot, future vs. future, spot vs. future or future vs.
spot prices of the same commodity. Here, the third hypothesis is also satisfied.
From the above results, it is found out that the differences in the relative importance of the spot and future prices in the price discovery role in the financial markets for the energy and agricultural commodities including precious metals. Moreover, it is important to understand and investigate the price discovery process of both the spot and future markets so as to guide and help the policy makers and market participants to formulate the efficient policies and improve the efficiencies of both markets. Moreover, the commodities like crude oil, natural gas, gold and silver have an important role in the spot and future market since they are the globally traded commodities with high risks thus raising the importance of the use of derivatives. Likewise, price fluctuations of the commodities directly impact on the personal life of everyone plays a vital role in the economy of the country should be realized.
Masih and Masih (2002) suggested that in the presence of either a non-stationary risk premium or a non-non-stationary convenience yield there exists no cointegration of commodity markets. Thus, from this point of view we can explain that for all the commodities (cocoa, coffee, natural gas, gold and silver) except crude oil there is the presence of the properties of the convenience yield and risk premium.
Similarly, the idea can also be generated that geopolitical plays a vital role in the spot and future markets which can completely twirled out the market scenario in a blink.
In addition, this study could be furthermore extended to observe the situation of spot and future prices of other major commodities focusing on the emerging markets since, these markets hugely affect the global business and comprise the huge space in the global market.
This paper will facilitate the academician, researchers, policy makers, financial analyst, and market players to know the actual value and forecast the outcomes of introduction the options in the global financial market. Moreover,
as Batra (2004) highlighted the fact that estimations of market volatility will help in this matter as it is considered as the barometer of the susceptibility of financial risks. Similarly, this paper will help portfolio managers in identifying the risks and hedge them by making efficient portfolios along with the portfolio diversification and creating arbitrage opportunities. If the company or an individual wants to utilize the new information on the movement of the future prices to enter in the hedging process, it is thus suggested to clearly overview the price movements or the relationships between the prices. Besides these, future contract is considered as one of the most important hedging instruments in a hedging contract since it highly reduces the business failure rates with making the availability of wide range of products in the financial markets. It has helped the companies to invest in resourceful but valuable production technologies and relocation of risks to those who are willing to bear and handle them (Culp, 2009). So as to reduce the spot price volatility future prices can be used in the financial market since the future market increases the overall market depth and in formativeness which are important for price discovery and transfer the risks.
References
Ab, Rahman, N. N. (2012). The Cointegration Analysis on the Spot Prices of the Malaysian Crude palm Oil Future Market, International Journal of Economics and Fianance, Vol. 4, Issue. 7, pp. 95-104.
Ahmad, H., Z. S., & Shah, A. I. (2010). Impact of Futures Trading on Spot Price Volatility: Evidence from Pakistan. International Research Journal of Finance and Economics (59), 145-165.
Almadi, S. M., Zhang, B. (2011). Lead-lag Relationship between World Crude Oil Benchmarks: Evidence from West Texas Intermediate, Brent, Dubai and Oman.
International Research Journal of Finance and Economics, Issue 80, pp. 13-26.
Asche, F., & Guttormen, G. ( 2002.). Lead Lag Relationships between Futures and Spot Prices. Institute for Research in Economics and Business Administration, Working Paper .
Asche, F., & Guttormsen, G. A. (2002). Lead Lag Relationship between Futures and Spot Prices. Institutue for Research in Economics and Business Administration , 1-25.
Awe, O. O. (2012). On Pairwise Granger Causality Modeling and Econometric Analysis of Selected Economic Indicator. Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria. Pp. 1-17.
Bandivadekar, S., & Gosh, S. (2003). Derivatives and Volatility on Indian Stock Markets. Reserve Bank of India Occasional Papers 24 , 187-201.
Batra, A. (2004). Stock Return Volatility Pattern in India. Indian Council of Research on International Economic Relations, Working Paper.
Bekiros, S., & Diks, C. (2008). The Relationship between Crude Oil Spot and Futures Prices: Cointegration, Linear and Nonlinear Causality. Energy Economics (30), 2673–
2685.
Bigman, D., Goldfarb, D., & Schechetman , E. (1983). Future Market Effeciency and the Time Content of Information Sets. Journal of Future Markets, Vol. 3, Issue, 3, pp.
321-334.
Blose, L. (2009). Cost of Carry and Expected Inflation,. Journal of Economics and Business, Forthcoming.
Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroscedasticity.
Journal of Econometrics 31 , 307-327.
Brooks, C. (2008). Introductory Econometrics for Finance. The United States of America Cambridge University Press, New York , 1-641.
Brooks, C., Rew, A., & Ritson, S. (2001). A Trading Strategy Based on the Lead‐Lag Relationship between the Spot Index and Futures Contract for the FTSE 100.
International Journal of Forecasting (17), 31-44.
Bruce, H., Sloan, M., & Leon, M. (2003). Natural Gas and Energy Price Volatility.
Energy and Environmental Analysis, Inc. Prepared for the Oak Ridge National .
Chinn, M., M, L., & Coibion., O. (2005). The Predictive Content of Energy Futures: An Update on Petroleum, Natural Gas, Heating Oil and Gasoline. National Bureau of Economic Research Working Paper No. 11033.
Chinn, M., Leblanc, M & Coibion, O. (2001). The Predictive Characteristics of Energy Futures: Recent Evidence for Crude Oil, Natural Gas, Gasoline, and Heating Oil.
UCSC Economics working paper No. 490.
Coibion, O., & Chinn, D, M. (2009). The Predictive Content of Commodity Futures. La Follette School of Public Affairs Working Paper No. 2009-016.
Cuddington, J. & Wang, Z. (2006). Assessing the Degree of Spot Market Integration for U.S. Natural Gas: Evidence from Daily Price Data. Journal of Regulatory Economics, 29, pp. 195-210.
Culp., L. (2009). The Social Functions of Derivatives. Financial Derivatives .
Dan, H. Forecasting with Structural Models and VARs: Relative Advantage and the Client Connection.
David, R., Chaudary, M., & Koch, T. (2000). Do Macroeconomics News Release Affect Gold and Silver Prices. Journal of Economics and Business , 5 (52), 405-421.
Dawson, P., Sanjuan, A., & White, B. (2010). Structural Breaks and the Relationship Between Barley and Wheat Futures Prices on the London International Financial Futures Exchange. Review of Agricultural Economics (28), 585-594.
Debasish, S. (2009). Effect of Futures Trading on Spot Price Volatility: Evidence for NSE Nifty Using GARCH. The Journal of Risk Finance 10 , 67-77.
Edwards, R. (1988). Does Futures Trading Increase Stock Market Volatility? Financial Analysts Journal 44. , 63-69.
Engle, R. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of Variance of United Kingdom. Econometrica 50 , 987-1007.
Engle, R. F., & Granger, C. (1987). Cointegration and Error Correction:
Representation, Estimation, and Testing. Econometrica (55), 251-276.
Fama, F. F., & French, R. K. (1987). Commodity Futures Prices: Some Evidence on Forecast Power, Premiums, and the Theory of Storage. The Journal of Business , 60 (1), 55-73.
Foster, A. J. (1996). Price Discovery in Oil Markets: A Time Varying Analysis of the 1990-91 Gulf Conflict. Energy Economics (18), 231-246.
Garbade, K. D., & Silber, W. L. (1983). Price Movement and Price Discovery in Futures and Cash markets. Review of Economics and Statistics (65), 289-297.
Garcia, P., & Leuthold, R. (2004). A selected Review of Agricultural Commodity Futures and Options Markets. European Review of Agricultural Economics (31), 235-272.
Gebre-Mariam, Y. (2011). Testing for Unit Roots, Causality, Cointegration, and Efficiency: The Case of theNorthwest US Natural Gas Market. . Energy (36), 3489-3500.
Giot, P. (2003). The Information Content of Implied Volatility in Agricultural Commodity Markets. Journal of Future Markets (23), 441-454.
Goodman, B. (1956). The Price of Gold and International Liquidity. J. Finance (11), 15–28.
Granger, C. (1986). Developments in the Study of Cointegrated Variables. Oxford Bulletin of Economics and Statistics (48), 213-227.
Granger, C., & Newbold, P. (1974). Spurious Regression in Econometrics. Journal of Econometrica , 2 (55), 251-276.
Hair, J. F., Anderson, R. E., Tatham, R. L., & Black, W. (1988). Multivariate Data Anaysis (5 ed.). Prentice Hall, USA.
Hernandez, M. & Torero, M. (2010). Examining the Dynamic Relationship between Spot and Future Prices of Agricultural Commodities. International Food Policy Research Institute, pp. 1-52.
Hendry, D., & Juselius, K. (1999). Explaining Cointegration Analysis: Part1. European University Institute, Florence.
Hernandez, M., & Torero, M. (2010). Examining the Dynamic Relationship between Spot and Future Prices of Agricultural Commodities. International Food Policy Research Institute, Discussion Paper 00988 , 1-52.
Hokkio, C., & Rush, M. (1989). Market Efficiency and Cointegration: An Application to Sterling and Deutshmark Exchange rates. Journal of International Money and Finance (8), 75-88.
Houthakker, H., Newman, P., Milgate, M., & Eatwell, J. (1992). Futures Trading. The New Palgrave Dictionary of Money and FInance , 2, 211-213.
Huang, N. B., Yang, C. W. & Hwang, M.J. (2009). The Dynamics of a Nonlinear Relationship between Crude Oil Spot and Future Prices: A Multivariate Threshold Regression Approach. Energy Economics, Issue 31, pp. 91-98.
Jackline, S., & Deo, M. (2011). Lead-Lag Relationship between the Futures and Spot Prices. Journal of Economics and International Finance , 3 (7), 424-427.
Kaufmann, R., & Ullman, B. (2009). Oil Prices, Speculation, and Fundamentals:
Interpreting Causal Relations Among Apot and Future Prices. Energy Economics (31), 550-558.
Kawaller, I., Koch, P., & Koch, T. (1998). The Relationship between the S&P 500 Index and the S&P 500 Index Futures Prices. Federal Reserve Bank of Atlanta Economic Review , 3 (73), 2-10.
Kebede, Y. (1993). Causality and Efficiency in the Coffee Futures Market. Journal of International Food and Agribusiness Marketing. , 1 (5), 55–72.
Kebede, Y. (1992). Causality and Efficiency in the Coffee Future Markets. Journal of International Food and Agribusiness Marketing, Vol. 5, Issue 1, pp. 55-71.
Khan, S. (2006.). “Role of the Futures Market on Volatility and Price Discovery of the Spot Market: Evidence from Pakistan's Stock Market". The Lahore Journal of Economics (11), 107-121.
Kofi, T.A. (1973). A Frame Work Comparing the Efficiency of Future Markets. Amer.
J. Ager. Econ., Vol. 4, Issue 55, pp. 584-594.
Koontz, S., Garcia, R., & Hudson, M. A. (1990). Dominant-Satellite Relationship between Live Cattle Cash and Future Marekts. The Journal of Future Markets (10), 123-136.
Kuiper, W., Pennnings, J., & Meulenberg, M. (2002). Identification by Full Adjust Adjustment: Evidence from the Relationship between Futures and Spots Prices.
European Review of Agricultural Economics (29), 67-84.
Kumar, M. (1992). The Forecasting Accuracy of Crude Oil Futures Prices. IMF Staff Papers 39 (2), 432-461.
Kwok, S. S. (2012). A Nonparametric Test of Granger Causality in Continuous Time.
Cornell University. pp. 1-89.
Lee, C. C., & Zeng, H. J. (2011). Revisiting the Relationship between Spot and Future Oil Prices: Evidence from Quantile Cointegrating Regression, Energy Economics, Issue 33, pp. 924-935.
Lee, C. W. (2012). Cointegration and Granger Causality Tests of Exchange Rate of Euro and Hong Kong Stock Market Index Interactions. International Research and Journal of Finance and Economics, Issue 91, pp. 119-122.
Leuthold, R. M. (1974). The Price Performance of the Future Market of a Non-Storable Commodity: Live Beef Cattle, American Journal of Agricultural Economics 56 (May), pp. 271-279
Lin, L. J. (2008). Notes on Testing Causality. Institute of Economics, Academia Sinica Department of Economics, National Chengchi University. pp. 1-20.
Liu, Y., & Mohammad, B. T. (2012). A Survey of Granger Causality: A computational view.
Ma, C. (1989). Forecasting Efficiency of Energy Futures Prices. Journal of Futures Market , 5 (9), 393-419.
Mariam, K. Y. (2011). Testing for Unit Roots, Causality, Cointegration and Efficiency:
The case of the Northwest US Natural Gas Market. Issue 36, pp. 3489-3500.
Martin, L., & Garcia, P. (1981). The Price‐forecasting Performance of Futures Markets for Live Cattle and Hogs: A Disaggreated Analysis. American Journal of Agricultural Economics (63), 209-215.
Masih, A.M.M., Masih, R. (2002). Propagative Causal Price Transmission Among International Stock Markets: Evidence from the Pre and Post Globalization Period.
Global Finance Journal, Vol. 13, pp. 63-91.
Maslyuk, S., & Smyth, R. (2009). Cointegration between Oil Spot and Future Prices of the Same and Different Grades in the Presence of Structural Change. Elsevier , 37, 1687-1693.
Maslyuk, S., & Smyth, R. (2009). Cointegration between Oil Spot and Future Prices of the Same and DifferentGrades in the Presence of Structural Changes. Energy Policy (37), 1687-1693.
Mohan, S., & Love, J. (2004). Coffee Futures: Role in Reducing Coffee Producers’
Price Risk. Journal of International Development (16), 983‐1002.
Moosa, I. (2002.). Price Discovery and Risk Transfer in the Crude Oil Futures Market:
Some Structural Time Series Evidence. Economic Notes By Banca Monte dei Paschi di Siena SpA (31), 155-165.
Moosa, I., McAleer, M., Miller, P., & Leong, K. (1996). An Econometricmodel of Price Determination in the Crude Oil Futures Markets. Proceedings of the Econometric Society Australasian meeting , 3, 373-402.
Newberry, D., Newman, P., Milgate, M., & Eatwell, J. (1992). Futures Markets:
Hedging and Speculation. The New Palgrave Dictionary of Money and Finance , 2, 207-210.
Oellermann, C., Brorsen, B., & Farris, P. (1989.). Price discovery for Feeder Cattle. . The Journal of Future Markets (9), 113-121.
Oxfam. (2001). Coffee Market Report. Oxford.
Pindyck, R. (2001). The Dynamics of Commodity Spot and Futures Markets: A primer.
Energy Journal , 22 (3), 1-29.
Quan, J. (1992). Two Step Testing Procedure for Price Discovery Role of Future Prices. The Journal of Future Markets , 18, 297-305.
Quan, J. (1992). Two Step Testing Procedure for Price Discovery Role of Futures Prices. The Journal of Futures Markets (12), 139-149.
Rajaraman, I. 1(986). Testing the Rationality of Future Prices for Selected Least Developed Countries Agricultural Exports. Journal of Future Market, Vol. 6, Issue 4, pp. 523-540.
Schroeder, T., & Goodwin, B. (1991). Price Discovery and Cointegration for Live Hogs. The Journal of Future Markets (11), 685-696.
Schwarz, T. V., & Szakmary, A. G. (1994). Price discovery in Petroleum Markets:
Arbitrage, Cointegration, and the Time Interval of Analysis. The Journal of Future Markets (14), 147-167.
Seghal, S., Rajput, N., & Dua, R. K. ((2012)). Future Trading and Spot Market Volatility: Evidence from Indian Commodity Markets. Asian Journal of Finance and Accounting. , 4 (2), 199-217.
Silvapulle, P., & Moosa, I. (1999). The Relationship between the Spot and Futures Prices: Evidence from the Crude Oil Market. Journal of Future Markets (19), 175-193.
Sjaastad, L. (2008). The Price of Gold and the Exchange Rate Once Again. Resource Policy , 2 (33), 118-124.
Solt, M., & Swanson, P. (1981). On the Efficiency of the Markets for Gold and Silver. . J. Business (54), 453-478.
Stein, J. (1987). Information Externalities and Welfare Reducing Speculation. Journal of Political Economy 95 , 1123-1145.
Stoll, H. R., & Whaley, R. E. (1990). The Dynamic of Stock Index and Stock Index Futures Returns. Journal of Future Market. , 25 (4), 441-468.
Tully, E., & Lucey, B. (2008). A Power GARCH Examination of the Gold Market.
Research in International Business and Finance, Vol. 21, pp. 316-325.
Vogelvang, E. (1992). Hypotheses Testing Concerning Relationships between Spot prices of Various Types of Coffee, Journal of Applied Econometrics, Vol. 7, pp. 191-201.
Wahab, M., & Lashgari, M. (1993). Price Dynamics and Error Correction in Stock Index and Error Correction in Stock Index and Stock Index Future Markets: A Cointegration Approach. Journal of Economics (66), 225-250.
Walls, D. W. (1995). Competition, Prices, and Efficiency in the Deregulated Gas Pipeline Network: A Multivariate Cointegration Analysis. Journal of Energy and Development, 19, pp. 1-14.
Yang, J., Bessler, D., & Leatham, D. (2001). Asset Storability and Price Discovery in Commodity Future Markets: A New Look. Journal of Futures Markets (21), 279-300.
Yohannes, M. G. (2011). Testing for Unit Roots, Causality, Cointegration, and Effeciency: The Case of the Northwest US Natural Gas Market. Elsevier (36), 3489-3500.
APPENDICES
APPENDIX 1.
UNIT ROOT TEST BEFORE FIRST DIFFERENCES I. Spot Prices
a. cocoa_spot
Null Hypothesis: COCOA_SPOT has a unit root Exogenous: Constant
Lag Length: 1 (Automatic - based on SIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -1.912965 0.3265 Test critical values: 1% level -3.432092
5% level -2.862195 10%level -2.567163
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(COCOA_SPOT) Method: Least Squares
Date: 01/28/13 Time: 15:29
Sample (adjusted): 3/03/2000 2/27/2013 Included observations: 3389 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
COCOA_SPOT(-1) -0.001911 0.000999 -1.912965 0.0558 D(COCOA_SPOT(-1)) -0.083416 0.017120 -4.872477 0.0000
C 4.286249 2.134546 2.008038 0.0447
R-squared 0.008160 Mean dependenvar 0.412842 Adjusted R squared 0.007574 S.D. dependent var 42.53885 S.E. of regression 42.37744 Akaike info criterion 10.33199 Sum squared resid 6080740. Schwarz criterion 10.33742 Log likelihood -17504.56 Hannan-Quincriter. 10.33393 F-statistic 13.92856 Durbin-Watson stat 1.998874 Prob(F-statistic) 0.000001
b. coffee_spot
Null Hypothesis: COFFEE_SPOT has a unit root Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -1.186958 0.6823 Test critical values: 1% level -3.432091
5% level -2.862195 10% level -2.567162
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(COFFEE_SPOT) Method: Least Squares
Date: 01/28/13 Time: 15:32
Sample (adjusted): 3/02/2000 2/27/2013 Included observations: 3390 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
COFFEE_SPOT(-1) -0.000863 0.000727 -1.186958 0.2353
C 0.001024 0.000905 1.130621 0.2583
R-squared 0.000416 Mean dependent var 6.49E-05 AdjustedRsquared 0.000121 S.D. dependent var 0.023817 S.E. of regression 0.023815 Akaike info criterion -4.636377 Sum squared resid 1.921587 Schwarz criterion -4.632761 Log likelihood 7860.659 HannanQuinncriter. -4.635084 F-statistic 1.408869 Durbin-Watson stat 1.964024 Prob(F-statistic) 0.235328
c. crude_oil_spot
Null Hypothesis: CRUDE_OIL_SPOT has a unit root Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -0.994072 0.7575
Test critical values: 1% level -3.432091 5% level -2.862195 10% level -2.567162
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(CRUDE_OIL_SPOT) Method: Least Squares
Date: 01/28/13 Time: 15:33
Sample (adjusted): 3/02/2000 2/27/2013 Included observations: 3390 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
CRUDE_OIL_SPOT(1) -0.000707 0.000711 -0.994072 0.3203
C 0.068410 0.049353 1.386121 0.1658
R-squared 0.000292 Mean dependent var 0.025006 Adjusted R-squared -0.000003 S.D. dependent var 1.339555 S.E. of regression 1.339557 Akaike info criterion 3.423145 Sum squared resid 6079.474 Schwarz criterion 3.426761 Log likelihood -5800.231 Hannan-Quinn criter. 3.424438 F-statistic 0.988179 Durbin-Watson stat 1.907600 Prob(F-statistic) 0.320259
d. gold_spot
Null Hypothesis: GOLD_SPOT has a unit root Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic 0.397134 0.9829 Test critical values: 1% level -3.432091
5% level -2.862195 10%level -2.567162
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(GOLD_SPOT) Method: Least Squares
Date: 01/28/13 Time: 15:34
Sample (adjusted): 3/02/2000 2/27/2013 Included observations: 3390 after adjustments Variable Coefficient
Std.
Error t-Statistic Prob.
GOLD_SPOT(-1) 0.000157 0.000395 0.397134 0.6913
C 0.287616 0.348348 0.825657 0.4091
R-squared 0.000047 Mean dependent var 0.404546 Adjusted R-squared -0.000249 S.D. dependent var 10.83741 S.E. of regression 10.83876 Akaike info criterion 7.604724 Sum squared resid 398017.9 Schwarz criterion 7.608340 Log likelihood -12888.01 HannanQuinncriter. 7.606017 F-statistic 0.157715 Durbin-Watson stat 2.001814 Prob(F-statistic) 0.691294
e. nat_gas_spot
Null Hypothesis: NAT_GAS_SPOT has a unit root Exogenous: Constant
Lag Length: 13 (Automatic - based on SIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -8.622396 0.0000 Test critical values: 1% level -3.432099
5% level -2.862198
10% level -2.567164
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(NAT_GAS_SPOT) Method: Least Squares
Date: 01/28/13 Time: 15:34
Sample (adjusted): 3/21/2000 2/27/2013 Included observations: 3377 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
NAT_GAS_SPOT(-1) -0.308991 0.035836 -8.622396 0.0000 D(NAT_GAS_SPOT(-1)) -0.593655 0.037200 -15.95860 0.0000 D(NAT_GAS_SPOT(-2)) -0.514714 0.037896 -13.58220 0.0000
f. silver_spot
Null Hypothesis: SILVER_SPOT has a unit root Exogenous: Constant
Lag Length: 7 (Automatic - based on SIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -0.885676 0.7933 Test critical values: 1% level -3.432095
5% level -2.862197 10% level -2.567163
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(SILVER_SPOT) Method: Least Squares
Date: 01/28/13 Time: 15:35
Sample (adjusted): 3/13/2000 2/27/2013 Included observations: 3383 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(NAT_GAS_SPOT(-3)) -0.488060 0.038149 -12.79342 0.0000 D(NAT_GAS_SPOT(-4)) -0.460970 0.038167 -12.07786 0.0000 D(NAT_GAS_SPOT(-5)) -0.415108 0.037890 -10.95568 0.0000 D(NAT_GAS_SPOT(-6)) -0.366177 0.037297 -9.817898 0.0000 D(NAT_GAS_SPOT(-7)) -0.312400 0.036282 -8.610424 0.0000 D(NAT_GAS_SPOT(-8)) -0.260931 0.034780 -7.502397 0.0000 D(NAT_GAS_SPOT(-9)) -0.224427 0.032764 -6.849788 0.0000 D(NAT_GAS_SPOT(-10)) -0.174850 0.030193 -5.790992 0.0000 D(NAT_GAS_SPOT(-11)) -0.140264 0.027044 -5.186504 0.0000 D(NAT_GAS_SPOT(-12)) -0.114786 0.023132 -4.962177 0.0000 D(NAT_GAS_SPOT(-13)) -0.070513 0.017210 -4.097171 0.0000
C 810.0819 106.5830 7.600477 0.0000
R-squared 0.451412 Mean dependentvar 1.007243 Adjusted R-squared 0.449127 S.D. dependent var 3949.608 S.E. of regression 2931.430 Akaike info criterion 18.80880 Sum squared resid 2.89E+10 Schwarz criterion 18.83601 Log likelihood -31743.66 Hannan-Quincriter. 18.81853 F-statistic 197.6043 Durbin-Watson stat 2.003141 Prob(F-statistic) 0.000000
SILVER_SPOT(-1) -0.000699 0.000789 -0.885676 0.3759 D(SILVER_SPOT(-1)) -0.110491 0.017094 -6.463843 0.0000 D(SILVER_SPOT(-2)) -0.007372 0.017194 -0.428770 0.6681 D(SILVER_SPOT(-3)) -0.036938 0.017196 -2.148074 0.0318 D(SILVER_SPOT(-4)) 0.028862 0.017202 1.677840 0.0935 D(SILVER_SPOT(-5)) -0.007806 0.017196 -0.453965 0.6499 D(SILVER_SPOT(-6)) -0.024747 0.017196 -1.439122 0.1502 D(SILVER_SPOT(-7)) 0.123727 0.017112 7.230581 0.0000
C 0.016909 0.013144 1.286422 0.1984
R-squared 0.032045 Mean dependent var 0.007334 Adjusted R-squared 0.029750 S.D. dependent var 0.463550 S.E. of regression 0.456603 Akaike info criterion 1.272650 Sum squared resid 703.4313 Schwarz criterion 1.288949 Log likelihood -2143.687 Hannan-Quinn criter. 1.278477 F-statistic 13.96238 Durbin-Watson stat 1.997734 Prob(F-statistic) 0.000000
ii. Future Prices g. cocoa_fut
Null Hypothesis: COCOA_FUT has a unit root Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=14)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -1.974183 0.2985 Test critical values: 1% level -3.432091
5% level -2.862195 10% level -2.567162
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(COCOA_FUT) Method: Least Squares
Date: 01/28/13 Time: 15:37
Sample (adjusted): 1/04/2000 12/31/2012 Included observations: 3390 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
COCOA_FUT(-1) -0.001913 0.000969 -1.974183 0.0484
C 4.138859 2.011678 2.057416 0.0397
R-squared 0.001149 Mean dependent var 0.411209 Adjusted R-squared 0.000854 S.D. dependent var 40.42110
R-squared 0.001149 Mean dependent var 0.411209 Adjusted R-squared 0.000854 S.D. dependent var 40.42110